Symbolic Computation: Poincare's inequality - geometric and analytic connections

Dr. Clemens Pechstein

May 10, 2011, 2 p.m. AS 50

Poincare's inequality allows to estimate the L2 norm of a function over a domain
by a constant factor times the L2 norm of its gradient, provided that the function
has a vanishing mean value. The constant factor is related to the second eigenvalue
of the Laplace operator on the domain and it is difficult to be determined.
In this talk, I will review results by Maz'ya and John which relate the Poincare
constant to geometric quantities associtated to the domain. Also, I would like to
present results by Rob Scheichl and myself that allow to estimate the Poincare
constant of domains built from finite element meshes.